# FORUM

### ‘Hear, hear’: British Parliament debates quadratic equations

#### By E. Andrew Boyd

British Parliament considered quadratic equations a “vital philosophical question.”

It was a topic of such magnitude that in 2003 the British Parliament took it up for debate. At issue were public comments made by the head of the schoolteachers union. The union head asked why students were being taught irrelevant topics, and as an example pointed to quadratic equations. Official records of the parliamentary debate appear under the simple yet apt title “Quadratic Equations.”

The fact that quadratic equations, in any form, could garner the attention of Britain’s highest legislative body is itself remarkable. Yet even more remarkable is the mathematical detail with which the topic is deliberated.

In his opening statement, Parliamentary Member Tony McWalter not only gives numerical examples of quadratic equations, he reminds those present that their solution leads us to confront the square root of -1. And he undertakes his rhetorical venture with the aim of raising “the vital philosophical questions that governments of all persuasions find it too easy to ignore.”

Quadratic equations, a “vital philosophical question”? A poll of students would likely find “needless frustration” a more common response than “vital” anything. But if so, it’s certainly not because quadratic equations are inherently devoid of interest or application.

Quadratic equations arise in problems as simple as determining areas; a topic of relevance, for example, when calculating taxes on landholdings. Such problems were common as early as 2000 B.C. in Babylonia, and clay tablets dating to that period show the Babylonians used what was essentially the quadratic formula to solve them. And throughout history many different cultures dealt with quadratic equations long before the Greeks latched onto them. Egypt. China. India. Quadratic equations kept popping up because they arose in so many practical contexts.

Much later, in the sixteenth century, Galileo made the monumental discovery that the distance an object falls as a function of time is described by a quadratic equation. Building on the work of Galileo and Kepler, Newton’s universal law of gravitation related the gravitational force between two objects via one of the most important quadratic equations of all time.

So why have quadratic equations become such villains? Perhaps the problem has less to do with the equations themselves than their dreaded cohort: the quadratic formula. The formula is intended to simplify students’ lives by providing an easy means to find the desired x hidden behind an algebraic expression. Unfortunately, for most students (and apparently many teachers) the quadratic formula has become an exercise in rote memorization. Sadly, this obscures the practical and historical significance of quadratic equations.

And that’s why the honorable Mr. Tony McWalter stood before the House of Commons in defense of “mathematics in general [and] quadratic equations in particular.” And in an entertaining yet serious commentary, he invoked name after name of prominent intellectual figures to make his case. Hume. Galileo. Kepler. Archimedes. Euclid. de Broglie. Schrödinger. Hawking. McWalter’s plea was impassioned.

“Hear, hear,” cried the lone voice of the honorable Mrs. Eleanor Laing.

“Oh dear,” replied McWalter. “I would like to have support from elsewhere as well.”

As the debate wound down, it was the honorable Alan Johnson, Minister for Lifelong Learning, Further and Higher Education, who had the last word. Quoting none other than Napoleon Bonaparte, he shared a brutally practical interpretation of the importance of math: “The advancement and perfection of mathematics are intimately connected with the prosperity of the state.”

To which I can only add, “hear, hear.”

Andrew Boyd, INFORMS Fellow and INFORMS VP of Marketing, Communications and Outreach, was an executive and chief scientist at an analytics firm for many years. He can be reached at e.a.boyd@earthlink.net.

#### References

1. The record of the debate can be found in Hansard, United Kingdom House of Commons, 26 June 2003, Columns 1259-1269, 2003. See also http://www.parliament.the-stationery-office.co.uk/pa/cm200203/cmhansrd/vo030626/debtext/30626-20.htm. Accessed Feb. 4.
2. Budd, C and C. Sangwin, “101 Uses of a Quadratic Equation,” from the +plus magazine website (http://plus.maths.org/content/os/issue29/features/quadratic/index). Accessed Feb. 4.
3. Budd, C. and C. Sangwin, “101 Uses of a Quadratic Equation: Part II,” from the +plus magazine website (http://plus.maths.org/content/101-uses-quadratic-equation-part-ii). Accessed Feb. 4.
4. O’Connor, J. and E. Robertson, “An Overview of Babylonian Mathematics,” from the University of Saint Andrews MacTutor History of Mathematics Archive (http://www-history.mcs.st-and.ac.uk/HistTopics/Babylonian_mathematics.html). Accessed Feb. 4.